The present invention relates to the analysis of particles with multiply scattered light, and more particularly, but not exclusively, relates to the determination of size distribution and volume fraction of particles using photon migration techniques.
Today's chemical industry heavily relies on particulate or dispersed phase processes. The quality of many industrial products produced by these processes relates to the size distribution of the particles in terms of diameter or another designated dimension. For example, Particle Size Distribution (PSD) is highly relevant to the application, texture, and appearance of titanium dioxide based paint products. In addition, emulsion polymerization processes produce paints, various coatings, and synthetic rubbers to name only a few. Since emulsion polymerization involves the growth of suspended polymer particles. PSD measurements can yield insight into the extent of reaction and molecular weight distribution and can also provide means for product characterization. These measurements can also be adapted to many crystallization processes, such as in the food industry, pharmaceutics, agricultural products, and bulk chemicals. One way to optimize many of the processes involving a dispersion of particles is by providing on-line measurement of particle size distribution in combination with robust process control responsive to these measurements. Rawlings, J. B., Miller, S. M., and W. R. Witkowski, Model Identification and Control of Solution Crystallization Processes, Ind. Eng. Chem. Res., 32, 1275–1296 (1993); Farrell, R. J. and Y -C. Tsai, Nonlinear Controller for Batch Crystallization: Development and Experimental Demonstration, AlChE J., 41, 2318–2321 (1995); and Dimitratos, J., Elicabe, G., and C. Georgakis, Control of Emulsion Polymerization Reactors, AlChE J., 40, 1993–2021 (1994) are cited as additional sources of background information concerning chemical process control.
Despite the usefulness of PSD information, technology has not advanced such that these measurements can be made consistently under a wide variety of conditions and in a cost-effective manner. Moreover, the ability to determine PSD and the volume occupied by the dispersed particles (the “volume fraction”) through “on-line” observation of the particles as they participate in the process remains elusive. These limitations adversely impact the development of optimal process controls for batch, semi-batch, and continuous reactors. The absence of this on-line measurement capability also impedes accurate model verification important in the formulation of a control model for non-linear processes. Typically, the lack of accurate modeling coupled with the lack of robust measurements have forced the use of open-loop control based upon less efficient downstream measurements; adversely impacting quality and efficiency.
Several laboratory particle sizing techniques exist, such as size-exclusion chromatography, capillary hydrodynamic fractionation, and photosedimentation; however, these techniques cannot provide on-line information about the process. Similarly, several optical techniques have been developed to provide PSD information. One of these techniques involves turbidity measurements which monitor the attenuation of light at multiple wavelengths traveling through a sample along a straight line path (180° relative to the incident light). Because these measurements do not account for backscatter nor multiple scattering of light back into the path length, turbidity analysis is only effective for diluted samples such that the product of turbidity, τ, and pathlength, L, is less than about 0.3. In other words, the optical path of the sample is no less than about three times the mean distance between scattering particles. Van de Hulst, H. Light Scattering by Small Particles Dover Publications, New York (1983); J. Wang, and F. R. Hallet, Spherical Particle Size Determination by Analytical Inversion of the UV-Visible-NIR Extinction Spectrum, Appl. Optics, 35, 193–200 (1996); and J. Vavra, Antalik, J., and M. Liska, Application of Regression Analysis in Spectroturbidity Size Characterization Methods, Part. Part. Syst. Charact. 12, 38–41 (1995) are cited as sources of additional information concerning turbidity based systems.
Another optical approach is Dynamic Light Scattering (DLS), also termed quasi-elastic light scattering or photon correlation spectroscopy. DLS systems monitor the fluctuation of light intensity due to the Brownian motion of a single particle into and out of the near-field. From the time-dependence of intensity fluctuations, the particle diffusion coefficient can be computed and the radius obtained from the Stokes-Einstein equation. A statistical number of measurements of diluted and pretreated samples can provide a PSD. Notably, DLS techniques are often used as the laboratory “standard” for spherical particles having a diameter of less than 10 microns. Thomas, J. C. and V. Dimonie, Fiber Optic Dynamic Light Scattering from Concentrated Dispersions. 3: Particle Sizing in Concentrates, Appl. Optics., 29, 5332–5335 (1990), and U.S. Pat. Nos. 5,502,561 and 4,781,460 are cited as sources of additional background information concerning DLS techniques.
In still another approach, angular light scattering or “diffraction” measurements are employed which monitor the angular scatter of light at a single wavelength due to diffraction from a single particle. Using classical scattering theory and known refractive indices of fluid and particle, an equivalent radius can be computed from an inverse solution. Again, a statistical number of measurements can provide PSD's from diluted samples of particles.
Turbidity, DLS, and diffraction measurements all require careful calibration of the light source and detector to provide meaningful measurements. Also, the possibility that wavelength dependent sample absorbance will vary during normal process disturbances and feedstock changes threatens the accuracy of these techniques. More importantly, these approaches all require a relatively dilute sample compared to the usual process concentration in order to be effective.
Turbidity, DLS, and diffraction techniques suffer from other limitations which complicates on-line implementation. For example, on-line application of these techniques would require automated sampling procedures. For sizing solids, side stream measurements frequently create maintenance problems such as clogged pumps, conduits and filters within sampling devices. For sizing of liquid droplets, side stream measurements often induce coalescence and breakup. Furthermore the mechanical action of most automated sampling procedures may change the particle, crystal, or dispersed phase size distribution. Moreover, on-line measurements under these approaches may require substantial dilution, phase separation, or sample destruction to be effective.
One system which attempts to solve these problems is a laser reflection or “backscatter” technique, such as the PAR TEC 100 available from Laser Sensor Technology. This system includes a laser with a narrow beam focused directly into a polydisperse medium undergoing processing. The focal position is made to vibrate at a high rate so that the beam travels significantly faster than particles in the medium. In theory, particles intercept the beam and reflect light for a duration of time which is proportional to the particle size. The reflected light is detected and timed, and a particle size is inferred from this information. To reconstruct a size distribution, the instrument counts the number of times each size occurs. Besides the constraint on speed of the beam relative to particle motion, tests have shown that this system consistently measures small particles as too large and large particles as too small. Also, the range swept by the laser beam must be smaller than the smallest particle size to be measured.
Similar to DLS and diffraction measurements, laser reflection techniques are based upon discrete single particle measurements to reconstruct PSD. Laser reflection measurements are sensitive to erroneous positioning of the focal plane, contribution of higher order scattering, and sampling error brought about by the hydrodynamic partitioning of large particles away from the wall and sensor head. In addition, the measurements are reported not to be accurate with non-opaque particles or dispersed droplets. Sparks, R. G., and C. L. Dobbs, The Use of Laser Backscatter Instrumentation for On-Line Measurement of the Particle Size Distribution of Emulsions, Part. Part. Syst. Charact. 10, 279–289 (1993) provides additional information concerning this technique.
Turbidity, DLS, Diffraction, and Laser reflection are all limited to some extent by the multiple scattering of light by the particles. These systems attempt to confine this problem by sampling and dilution, or by adjusting various other system parameters. Also hampering the effectiveness of these techniques is the need to calibrate the equipment in situ. Process upsets, feedstock changes, or even normal batch process changes may invalidate the calibration. Depending upon the application, the sensor output for feedback control could be catastrophic absent proper calibration.
Thus, a need remains for a technique to analyze particles in a process stream which is self-calibrating and interrogates the process stream without requiring sampling or dilution. Preferably, this technique may be used to determine particle size distribution and volume fraction regardless of particle concentration level.